Blender 2.8 Beta (Linux Mint 19.1): No compatible GPUs found - Vega 64 Nitro+
You most probably have installed the open source driver stack that comes with Mint. 

On any GNU/Linux distribution, Blender only supports the official AMD proprietary drivers for rendering with OpenCL, meaning you will need to install one of the following AMD OpenCL drivers:


AMDGPU
AMDGPU-PRO


For Linux Mint, this might be a good start

There might be another method to just install the OpenCL part of the AMMDGPU-PRO driver, which is described here, but I don't have the  means to test it.